Statistical modelling of home range and larvae movement data

Abstract

In this thesis, we investigate two di erent approaches to animal movement modelling; nite mixture models, and di usion processes. These models are considered in two di erent contexts, rstly for analysis of data obtained in home range studies, and then, on a much smaller scale, modelling the movements of larvae. We consider the application of mixture models to home range movement data, and compare their performance with kernel density estimators commonly used for this purpose. Mixtures of bivariate normal distributions and bivariate t distributions are considered, and the latter are found to be good models for simulated and real movement data. The mixtures of bivariate t distributions are shown to provide a robust parametric approach. Subsequently, we investigate several measures of overlap for assessing site delity in home range data. Di usion processes for home range data are considered to model the tracks of animals. In particular, we apply models based on a bivariate Ornstein-Uhlenbeck process to recorded coyote movements. We then study modelling in a di erent application area involving tracks. Di usion models for the movements of larvae are used to investigate their behaviour when exposed to chemical compounds in a scienti c study. We nd that the tted models represent the movements of the larvae well, and correctly distinguish between the behaviour of larvae exposed to attractant and repellent compounds. Mixtures of di usion processes and Hidden Markov models provide more exible alternatives to single di usion processes, and are found to improve upon them considerably. A Hidden Markov model with 4 states is determined to be optimal, with states accounting for directed movement, localized movement and stationary observations. Models incorporating higherorder dependence are investigated, but are found to be less e ective than the use of multiple states for modelling the larvae movements.